Pressure

Introduction

Pressure is a fundamental concept in physics that plays a crucial role in various aspects of our daily lives. It is defined as the force applied per unit area. In other words, it is the amount of force distributed over a given area. Pressure is a scalar quantity and is measured in pascals (Pa) or newtons per square meter (N/m$^2$).

Pressure in Liquids

Key Terms:

• Hydrostatic Pressure: The pressure exerted by a fluid at rest due to the weight of the fluid above it.
• Pascal's Principle: States that a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.

Example:

Calculate the hydrostatic pressure at the bottom of a swimming pool that is 3 meters deep. Given that the density of water is 1000 kg/m$^3$ and acceleration due to gravity is 9.81 m/s$^2$.

Solution: The pressure at a depth in a liquid is given by $P = \rho gh$, where:

• $P$: Pressure
• $\rho$: Density of the liquid
• $g$: Acceleration due to gravity
• $h$: Depth

Substitute the values into the formula: $P = 1000 \times 9.81 \times 3 = 29430$ Pa

Therefore, the hydrostatic pressure at the bottom of the swimming pool is 29430 Pa.

Atmospheric Pressure

Key Terms:

• Atmospheric Pressure: The pressure exerted by the weight of the atmosphere on the Earth's surface.
• Barometer: An instrument used to measure atmospheric pressure.

Example:

Calculate the atmospheric pressure in a location where the barometer reading is 760 mmHg. Given that atmospheric pressure supports a column of mercury 760 mm high.

Solution: Convert the barometer reading from mmHg to pascal: 1 mmHg = 133.32 Pa

Therefore, atmospheric pressure = $760 \times 133.32 = 101325$ Pa.

Pressure in Gases

Key Terms:

• Boyle's Law: States that the pressure of a given mass of gas is inversely proportional to its volume at a constant temperature.
• Charles's Law: States that the volume of a given mass of gas is directly proportional to its temperature at constant pressure.

Example:

A gas has a volume of 4 L at a pressure of 2 atm. If the pressure is increased to 4 atm while keeping the temperature constant, what will be the new volume of the gas?

Solution: According to Boyle's Law, $P_1V_1 = P_2V_2$, where:

• $P_1$: Initial pressure
• $V_1$: Initial volume
• $P_2$: Final pressure
• $V_2$: Final volume

Substitute the values into the formula: $2 \times 4 = 4 \times V_2$

Solving for $V_2$: $V_2 = \frac{2 \times 4}{4} = 2$ L

Therefore, the new volume of the gas will be 2 L.

Common Mistakes

• Confusing pressure with force: Remember, pressure is force per unit area.
• Forgetting to consider the units: Always pay attention to the units when calculating pressure.
• Neglecting atmospheric pressure: Atmospheric pressure is an important factor in many physics problems.

Key Points

• Pressure is defined as force per unit area.
• Pressure in liquids is given by $P = \rho gh$.
• Atmospheric pressure is the pressure exerted by the weight of the atmosphere.
• Boyle's Law relates the pressure and volume of a gas at constant temperature.
• Charles's Law relates the volume and temperature of a gas at constant pressure.

Practice Questions

1. A liquid of density 800 kg/m$^3$ exerts a pressure of 4000 Pa at a certain depth. Calculate the depth of the liquid.

Answer: $P = \rho gh$ $4000 = 800 \times 9.81 \times h$ $h = \frac{4000}{800 \times 9.81} = 0.51$ m

2. If the volume of a gas at 2 atm is 6 L, what will be the volume at 3 atm pressure, assuming constant temperature?

Answer: $P_1V_1 = P_2V_2$ $2 \times 6 = 3 \times V_2$ $V_2 = \frac{2 \times 6}{3} = 4$ L

3. Explain the concept of atmospheric pressure and its measurement using a barometer.

Answer: Atmospheric pressure is the pressure exerted by the weight of the atmosphere on the Earth's surface. It is measured using a barometer, where the height of the mercury column in the barometer is a direct measure of atmospheric pressure.

4. State Boyle's Law and provide an example illustrating its application.

Answer: Boyle's Law states that the pressure of a given mass of gas is inversely proportional to its volume at a constant temperature. For example, if the volume of a gas is halved, the pressure will double, assuming constant temperature.

5. Calculate the pressure at the bottom of a lake that is 10 m deep, given that the density of water is 1000 kg/m$^3$.

Answer: $P = \rho gh$ $P = 1000 \times 9.81 \times 10 = 98100$ Pa